Problem: Simplify; express your answer in exponential form. Assume $y\neq 0, x\neq 0$. $\dfrac{{(y^{2})^{-3}}}{{(y^{5}x^{-5})^{-1}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{2}}$ to the exponent ${-3}$ . Now ${2 \times -3 = -6}$ , so ${(y^{2})^{-3} = y^{-6}}$ In the denominator, we can use the distributive property of exponents. ${(y^{5}x^{-5})^{-1} = (y^{5})^{-1}(x^{-5})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{2})^{-3}}}{{(y^{5}x^{-5})^{-1}}} = \dfrac{{y^{-6}}}{{y^{-5}x^{5}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-6}}}{{y^{-5}x^{5}}} = \dfrac{{y^{-6}}}{{y^{-5}}} \cdot \dfrac{{1}}{{x^{5}}} = y^{{-6} - {(-5)}} \cdot x^{- {5}} = y^{-1}x^{-5}$.